Latin squares are a classical and well-studied topic of discrete mathematics, and recently Takeuti and Adachi (IACR ePrint, 2023) proposed (2, n)-threshold secret sharing based on mutually orthogonal Latin squares (MOLS). Hence efficient constructions of as large sets of MOLS as possible are also important from practical viewpoints. In this letter, we determine the maximum number of MOLS among a known class of Latin squares defined by weighted sums. We also mention some known property of Latin squares interpreted via the relation to secret sharing and a connection of Takeuti-Adachi’s scheme to Shamir’s secret sharing scheme.

In network coding, for the case that the network topology is unknown completely, random linear network coding has been proposed as an acceptable coding technique. In this paper, we define average failure probability of random linear network coding in order to characterize the performance of random network coding, and then analyze this failure probability for different known topological information of network. We obtain several upper bounds on the failure probabilities, and further show that, for some networks, these upper bounds are tight or asymptotically tight. Moreover, if the more topological information of the network is utilized, the better upper bounds are acquired.

We discuss the problem of finding a dominant sequence for sending input data items from a low-end client to a server for computational intensive tasks under the realistic assumption of unpredictable communication behavior. Under this assumption, the client has to send the input data items using a specified sequence to maximize the number of computations performed by the server at any time. The sequence-finding problem is NP-hard for the general case. In this paper, we address three fundamental and useful applications: the product of two polynomials, matrices multiplication and Fast Fourier Transform. We show that the sequence-finding problems of the three applications can be solved optimally in linear time. However, we also show counter examples to rule out any possibility of finding a dominant sequence for sparse cases of the three applications. Finally, a simulation is conducted to show the usefulness of our method.

The present letter describes the estimation of the upper bounds of the correlation functions of a class of zero-correlation-zone sequences constructed from an arbitrary Hadamard matrix.

This paper presents upper bounds on the average bit error rate (BER) of coherent detection of PSK and differential detection of DPSK with adaptive arrays in fading environments. A model where a line of sight (LOS) component and Rayleigh distributed scattering components arrive at a receiver with specific arrival angles is used considering the correlation of signal between multiple antennas. The upper bounds are expressed in a simple matrix form using signal and interference-plus-noise correlation matrices. Examples for the case of 4-element adaptive arrays are given to illustrate the tightness and the application of this upper bounds.

A new upper hound on the error probability for maximum likelihood sequence estimation of digital signaling on intersymbol interference channels with additive white Gaussian noise is presented. The basic idea is to exclude all parallel error sequences and to exclude some of the overlapping error events from the union bound. It is shown that the new upper bound can be easily and efficiently computed by using a properly labeled error-state diagram and a one-directional stack algorithm. Several examples are presented that compare the new upper bound with bounds previously reported in the literature.

An idea of optimal output permutation of multiple-valued sum-of-products expressions is presented. The sum-of-products involve the TSUM operator on the MIN of window literal functions. Some bounds on the maximum number of implicants needed to cover an output permuted function are clarified. One-variable output permuted functions require at most p1 implicants in their minimal sum-of-products expressions, where p is the radix. Two-variable functions with radix between three and six are analyzed. Some speculations of maximum number of the implicants could be established for functions with higher radix and more than 2-variables. The result of computer simulation shows that we can have a saving of approximately 15% on the average using permuting output values. Moreover, we demonstrate the output permutation based on the output density as a simpler method. For the permutation, some speculation is shown and the computer simulation shows a saving of approximately 10% on the average.